"Fresh firing between the security forces and the holed-up terrorists took place at around 4.00 am. Intermittent firing continued for several hours since then," police sources said.
The security forces have maintained a tight cordon around the terrorists to prevent them from escaping.
The gunbattle broke out in Rajpora area of the district, 45 km from Srinagar, on Wednesday afternoon when a foot patrol of 44 Rashtriya Rifles came under fire from the terrorists.
A top terrorist of the Jaish-e-Mohammad outfit was killed in the encounter on Wednesday.
A police spokesman said the slain terrorist has been identified as self-styled divisional commander of JeM Altaf Baba alias Gazi Baba.
Baba's body was retrieved from the encounter site early in the morning and handed over to his family. The spokesman said Baba was involved in several terror-related incidents, including killing and kidnapping of civilians.
He was involved in the killing of civilians Nazir Ahmad Chopan and Mohammad Ahsan Wan in Kulgam district. He was also involved in abduction of local Shameem Ahmad Dar, the spokesman said.
He said Baba had also carried out several attacks on security forces in Rajpora area.
"Baba joined the JeM outfit in 2008. He was motivated by Sajad Afgani alias Ahsan Bhai of Pakistan to join terror ranks," the spokesman said.